Once it's downloaded extract the tar.gz file into a folder in your home directory (for example warzone2100).

Open up the terminal window (I use Ubuntu so a ctrl-alt-t shortcut works for me) and change to that directory (cd warzone2100)
then type ./configure into the terminal. This should check to see if you can compile it and will tell you what packages you need to install if you're missing them (sudo apt-get install <missing package name>).

Once ./configure runs through with no error messages, then you can go to the next step which is to type:
sudo make install
into the terminal window. This will compile the game and may take a few minutes. Once it's completed then type
./src/warzone2100
into the terminal window and that will start the game. Afterwards the game should start simply by typing warzone2100 into the terminal window.

The flavour of Linus I use is Ubuntu, so some of the commands for installing the packages may differ depending on the version of Linux you use, so remember, google is your friend.